Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 1. General Formulation and Predictions

Abstract

The transport coefficients of dense polymeric fluids are approximately calculated from the microscopic intermolecular forces. The following finite molecular weight effects are discussed within the Polymer-Mode-Coupling theory (PMC) and compared to the corresponding reptation/ tube ideas: constraint release mechanism, spatial inhomogeneity of the entanglement constraints, and tracer polymer shape fluctuations. The entanglement corrections to the single polymer Rouse dynamics are shown to depend on molecular weight via the ratio N/N e , where the entanglement degree of polymerization, N e , can be measured from the plateau shear modulus. Two microscopically defined non-universal parameters, an entanglement strength 1/α and a length scale ratio, δ = ξ ρ /b, where ξ ρ and b are the density screening and entanglement length respectively, are shown to determine the reduction of the entanglement effects relative to the reptation-like asymptotes of PMC theory. Large finite size effects are predicted for reduced degrees of polymerization up to N/N e ≤ 10 3 . Effective power law variations for intermediate N/N e of the viscosity, η ∼ N x , and the diffusion constant, D ∼ N −y , can be explained with exponents significantly exceeding the asymptotic, reptation-like values, x ≥ 3 and y ≥ 2, respectively. Extensions of the theory to treat tracer dielectric relaxation, and polymer transport in gels and other amorphous systems, are also presented.Macromolecules, accepted (May 1997).

Monte Carlo Simulation of Long Chain Polymer Melts: Crossover from Rouse to Reptation Dynamics

“…8). This behavior is similar to that expected from polymer mode-coupling theory [24][25][26]. The theory predicts two power laws: 1 − φ e (t) ∼ t 9/32 for τ e ≪ t ≪ τ R and 1 − φ e (t) ∼ t 3/8 for τ R ≪ t ≪ τ RR (τ RR = renormalized Rouse time < τ d ).…”

“…Both quantities are scaled by the N -dependences of Eqs. (22) and (25) to highlight deviations from Rouse behavior. The diffusion coefficient is compared with results from previous studies [34,35].…”

“…The ordinates were scaled by the chain length dependence expected from the Rouse model, i.e., τ ee /N 2 and ND [see Eqs. (22) and (25)]. The figure illustrates that neither τ ee nor D behave Rouse-like for small N or reptation-like for large N. A possible explanation for this finding is given by a recent reanalysis [36] of the crossover scaling from the semi-dilutesolution to the melt state of the bond-fluctuation model [34].…”

Chain dynamics in entangled polymers: Diffusion versus rheology and their comparison

“…Schweizer and coworkers developed a detailed theoretical account52, 53 of the zero‐shear viscosity and diffusion coefficient with the polymer mode coupling (PMC) theory 54–56. They found the self‐diffusion coefficient D s to converge to its reptative scaling N −2 at a smaller value of N / N e than that at which the zero‐shear viscosity converges to the scaling of N 3 .…”

Polymer dynamics in bimodal polyethylene melts: A study with neutron spin echo spectroscopy and pulsed field gradient nuclear magnetic resonance

“…The only tractable approximation-a renormalized Rouse theory 14 -stands in contradiction to experimental results for macroscopic quantities such as diffusion coefficient and viscosity, as well as to the results obtained by Richter et al 15 with NSE. Unfortunately the authors only applied their model in a more general form to macroscopic quantities; 16,17 a calculation of the dynamic structure factor is still missing.…”